Somos sequences are expressible as quadratic powers times theta functions, but these entail mysterious parameters empirically determined to make the first few terms come out right. An exception from arxiv.org/pdf/math/0703470 : RSolveInYourDreams[{a[n] == (a[-2 + n]^2 + a[-3 + n] a[-1 + n])/a[-4 + n], a[1] == 1, a[2] == 1, a[3] == -1, a[4] == Root[17 + 21 #1 - 5 #1^2 + 3 #1^3 + #1^4 &, 1]}, a[n], n] would give a[n]->ChebyshevU[-1 + n, 1/(2 Root[-1 - #1 + #1^4 &, 2]^(3/2))]* Root[-1 - #1 + #1^4 &, 2]^(1/2 (-1 + n^2)) featuring two nondescript quartic surds. Test: In[492]:= First /@ NestList[Append[Rest[#], (#[[4]] #[[2]] + #[[3]]^2)/#[[1]] // RootReduce] &, {1, 1, -1, Root[17 + 21 #1 - 5 #1^2 + 3 #1^3 + #1^4 &, 1]}, 7] Out[492]= {1, 1, -1, Root[17 + 21 #1 - 5 #1^2 + 3 #1^3 + #1^4 &, 1], Root[-11 + 36 #1 - 8 #1^2 - #1^3 + #1^4 &, 1], Root[89 - 731 #1 - 210 #1^2 - 18 #1^3 + #1^4 &, 2], Root[-379 - 12391 #1 + 2354 #1^2 - 134 #1^3 + #1^4 &, 2], Root[119 + 20913 #1 - 155 #1^2 + 51 #1^3 + #1^4 &, 1]} In[494]:= Table[RootReduce[ ChebyshevU[-1 + n, 1/(2 Root[-1 - #1 + #1^4 &, 2]^(3/2))]* Root[-1 - #1 + #1^4 &, 2]^(1/2 (-1 + n^2))], {n, 8}] Out[494]= {1, 1, -1, Root[17 + 21 #1 - 5 #1^2 + 3 #1^3 + #1^4 &, 1], Root[-11 + 36 #1 - 8 #1^2 - #1^3 + #1^4 &, 1], Root[89 - 731 #1 - 210 #1^2 - 18 #1^3 + #1^4 &, 2], Root[-379 - 12391 #1 + 2354 #1^2 - 134 #1^3 + #1^4 &, 2], Root[119 + 20913 #1 - 155 #1^2 + 51 #1^3 + #1^4 &, 1]} If ISC (etc?) tabulated the mysterious parameters in the theta formulas, maybe one day they'd suddenly become nonmysterious. --rwg